An object is placed on the principal axis of convex lens of focal length $10 cm$ as shown. A plane mirror is placed on the other side of lens at a distance of $20 cm$ . The image produced by the plane mirror is $5 cm$ inside the mirror. The distance of the object from the lens is………….cm.

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answer is 30.

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Detailed Solution

Image distance due lens = 20 – 5 = 15cm
We have $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$

$\begin{array}{l} \frac{1}{10} = \frac{1}{15} + \frac{1}{x} \Rightarrow \frac{1}{10} - \frac{1}{15} = \frac{1}{x} \\ x = 30 cm \end{array}$

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